The ranges are 1 100 1 1000 1 10000 1 100000 1 1000000 1 100

The ranges are:

[1, 100]

[1, 1000]

[1, 10000]

[1, 100000]

[1, 1000000]

[1, 10000000]

[7870000000, 7879999999]

[9390000000, 9399999999]

Find:

a)The last five prime numbers in the above 8 ranges

b)The first five prime numbers in ranges vii and viii.

c)Using the number of prime numbers for range (i) to (vi),

d) draw a graph that shows the number versus the maximal number in the range, the x-axis shall be log (base 10) of the number.

e)Include another curve for (n / ln n), where ln is nature log

Solution

#a)

Given : [1, 100]

factor of 97 = 1x97 => 97 is prime.

factor of 89 = 1x89 => 89 is prime.

factor of 83 = 1x83 => 83 is prime.

factor of 79 = 1x79 => 79 is prime.

factor of 73 = 1x73 => 73 is prime.

Hence, last five prime numbers in [1, 100] are : 97 , 89, 83, 79, 73 [ Answer ]